Network Address Translation.
Your ISP gives you one public IP address. It is assigned to your router. Your router has a pool of IPs it uses to assign to devices in your home (PC, wireless printer, game system, etc). NAT is what binds the two sets of IPs together. In this case, it's a one-to-many assignment. Yes, you can have one-to-one and other flavors, but most, if not all, home users are on a one-to-many NAT configuration.
The purpose is to conserve publicly routable IPs, but it also adds a layer of security.
Chris